Hint: try solving for t.
syms x y t
tsol = solve(x == cos(t) - y*sin(t),t)
So there are two solutions. Much of the time, a fully real solution will not exist. That will depend on the values of x and y.
subs(tsol,[x,y],[0.9991/1.02,2.1838/1.2544])
vpa(ans)
You can ignore the imaginary part of that, since it is essentially a VPA zero.
Alternatively, you could just use fzero.
txyfun = @(t,x,y) cos(t) - y*sin(t) - x;
x = 0.9991/1.02;
y = 2.1838/1.2544;
tfun = @(t) txyfun(t,x,y);
First, PLOT IT. Does a solution exist?
fplot(tfun)
yline(0)
So it would appear there are infinitely many solutions. fzero can find one of them. I don't even need to give it a brack around a root in this case.
[tval,fval,exitflag] = fzero(tfun,0)
